New breed - StackEdit
Stackedit (https://stackedit.io/) is a browser-based, markdown editor. It's simple enough for content creation: type on the left panel, see the result on the right.
It also offers a word count, although I had to look for it. On the lower end of the right panel, there's a vertical three dot icon. Touch that, and a box pops up with a panel including a charcter count. Touch that number, and get a word count. The panel will even stay on the screen. It doesn't seem to have a search function, or navigation.
Moreover, although this stores content in the local browser cache, it can be set to sync with Google Docs or Dropbox. Unlike some of the browser editors I've seen, it works well on mobile platforms. It is free, although it prompts you for a $5 donation.